ILAW Lesson Plan — Mathematics 6
Term 1 · Week 7 · Number and Algebra · five sessions × 45 minutes
| Learning Area | Mathematics |
| Grade Level | Grade 6 |
| Term / Week | Term 1, Week 7 |
| CG source | Quarter 1, competency 11 (p. 48) |
| Week Title | Make It a Fraction First — Multiplying Any Combination |
| Duration | 5 × 45 minutes |
| Format | ILAW — Intentions · Learning Experiences · Assessment · Ways Forward |
Two formats, two jobs. This is the week, in the format DepEd prescribes for the plan a teacher files. Its companion
lesson-plan.mdis Day 1 only, in the MATATAG Lesson Exemplar format, written at the depth of a teaching script — every question, every anticipated wrong answer, every timing. Use this one to plan and to file; open that one before you teach Monday.
⚠️ The ILAW field list is reported, not read. DO No. 009, s. 2026 is understood to prescribe ILAW as the single lesson plan template for SY 2026–2027, replacing both the Daily Lesson Log and the Detailed Lesson Plan, and to bar schools, divisions and regions from requiring any other. The four section names below are consistently reported; the exact sub-fields your division expects may differ. The order itself could not be downloaded in the environment this was built in — see
source-catalogue.md§8. Check against your division's own copy before filing.
I — INTENTIONS
A. Curriculum anchor
Quoted from the MATATAG Mathematics CG (DepEd, August 2023, p. 48):
Content standard. The learners should have knowledge and understanding of the four operations with different combinations of fractions, whole numbers, and mixed numbers.
Performance standard. By the end of the quarter, the learners are able to perform the four operations with different combinations of fractions, whole numbers, and mixed numbers.
Competency covered this week — quoted verbatim:
11. obtain products that result from multiplying different combinations of fractions, whole numbers, and mixed numbers.
Where the class is coming from. Grade 5 competency 8 — multiply a fraction by a fraction — is assumed secure. This week removes the restriction that both factors be proper fractions.
✅ Verified against the curriculum guide committed at
docs/research/source/.
B. What learners will be able to do, by day
| Day | Intention — by the end of the session, at least 80% of learners can… | Competency |
|---|---|---|
| 1 | Explain, using a rectangle, why 2½ × 1⅓ is not 2⅙ — and find what it actually is | 11 |
| 2 | Convert any mixed number to an improper fraction and multiply any two numbers by the single rule | 11 |
| 3 | Simplify before multiplying, and handle a whole number by writing it over 1 | 11 |
| 4 | Estimate the product first and use the estimate to catch their own errors | 11 |
| 5 | Choose the method themselves in a word problem, and justify the answer's size | 11 |
Day 1 does not teach the method. It destroys the wrong one. A class that is shown "make it improper, then multiply" on Monday will apply it correctly all week and revert to multiplying the whole parts the moment the topic is out of sight. The four-piece rectangle is what makes the reversion impossible.
C. Key idea and vocabulary
Make everything a fraction first. Then there is only one rule.
| Term | Meaning used this week |
|---|---|
| Mixed number | A whole and a part written together — 2½ |
| Improper fraction | A fraction whose numerator is at least its denominator — 5/2 |
| The same quantity | 2½ and 5/2 are not two numbers. They are one number, written twice |
| Simplify first | Cancel a common factor across the fraction bar before multiplying |
| Estimate | A quick, deliberately rough answer used to check the exact one |
The class sentence, repeated all week until it is automatic: "Make it a fraction. Then multiply. Then check the size."
D. Integration
| Strand | How it appears |
|---|---|
| EPP / TLE | Scaling a recipe by 1½; costing materials sold in fractional units |
| Araling Panlipunan | Land area: "the lot is 2¼ hectares; ⅔ of it is planted" |
| EsP / GMRC | Day 4's error-hunt is done in pairs; finding a partner's mistake is framed as help, not competition |
| English | Improper as a mathematical term with no negative meaning |
| 21st-century skills | Estimating as a habit of self-checking, not an extra task |
L — LEARNING EXPERIENCES
Every session is 45 minutes and runs complete with chalk and scrap paper alone. Digital artifacts are listed where they help; none is required.
Day 1 · The four-piece rectangle
Full teaching script:
lesson-plan.md. Summary only here.
| Phase | Min | What happens |
|---|---|---|
| Activating prior knowledge | 5 | Three Grade 5 products, timed: ⅔ × ¾, ⅗ × ½, ⅞ × ⅔. Secure ground first. |
| Establishing purpose | 6 | Board: 2½ × 1⅓. "Work it out." Most of the class will produce 2⅙ — whole times whole, part times part. Write 2⅙ on the board and do not mark it. Take a second answer if one is offered; write that too. |
| Developing understanding | 22 | Draw a rectangle 2½ wide and 1⅓ tall. Cut it with two lines into four pieces. Compute each: 2 × 1 = 2 · 2 × ⅓ = ⅔ · ½ × 1 = ½ · ½ × ⅓ = ⅙. Total 3⅓. Then the short route: 2½ = 5/2, 1⅓ = 4/3, 5/2 × 4/3 = 20/6 = 3⅓. Same answer, two ways. |
| Making generalisations | 7 | "Where did 2⅙ come from?" — it is two of the four pieces. The method did not add up; it left two pieces out. Land the sentence. |
| Evaluating | 5 | Exit ticket on 1½ × 2¼ — with the demand to say whether the answer should be more or less than 3. |
Independent practice, without devices — learners convert, multiply, simplify:
| Problem | As fractions | Product | Simplest form |
|---|---|---|---|
| 2½ × 1⅓ | 5/2 × 4/3 | 20/6 | 3⅓ |
| 1½ × ⅔ | 3/2 × 2/3 | 6/6 | 1 |
| 3 × ⅔ | 3/1 × 2/3 | 6/3 | 2 |
| 2¼ × 1⅕ | 9/4 × 6/5 | 54/20 | 2 7/10 |
| ⅘ × 2½ | 4/5 × 5/2 | 20/10 | 2 |
The last two rows are the ones to circulate for. Both give tidy answers from untidy inputs, and learners who reach 2 7/10 or 2 assume they have gone wrong. They have not.
Day 2 · One rule for everything
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Yesterday's five products, from memory or from the improper form. |
| Purpose | 5 | Board: 4 × 2⅗. "There is no fraction in the first number. Does the rule still work?" |
| Developing | 24 | Whole numbers: 4 = 4/1. So 4 × 2⅗ = 4/1 × 13/5 = 52/5 = 10⅖. Then the reverse conversions, drilled: 2⅗ → 13/5, 3¾ → 15/4, 1⅚ → 11/6, 5½ → 11/2. Then mixed × mixed, mixed × whole, whole × fraction, fraction × mixed — four shapes, one rule, worked in that order so the class sees the rule absorb each new case. |
| Generalising | 6 | Build the table in §C: every number in this topic can be written as a fraction, so there is nothing left to learn — only cases to recognise. |
| Evaluating | 5 | Exit ticket: 3⅓ × 1½ (= 10/3 × 3/2 = 30/6 = 5). |
Digital support: slides.html slides 6–10 animate the conversion.
game.html Round 1 is conversion only.
Day 3 · Simplify first
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Four conversions, timed. |
| Purpose | 5 | Board: 2⅘ × 1⅞ worked the long way — 14/5 × 15/8 = 210/40 — then simplified to 21/4 = 5¼. "Two hundred and ten. Is there less work available?" |
| Developing | 23 | Cancel before multiplying: the 5 with the 15, the 14 with the 8. 14/5 × 15/8 → 7/1 × 3/4 = 21/4 = 5¼. Same answer, numbers small enough to do in the head. Practise on four more. Then the warning: cancelling only ever works across the bar — top with bottom, never top with top. |
| Generalising | 7 | "Why is it allowed?" — because cancelling is dividing the top and the bottom by the same number, which is what equivalent fractions have always been. This is Grade 4 knowledge, arriving where it pays. |
| Evaluating | 5 | Exit ticket: 3⅗ × 1⅔, simplifying first (= 18/5 × 5/3 = 6). |
Day 4 · Estimate first, then check yourself
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Three products from Day 3. |
| Purpose | 5 | Board: 4⅞ × 2 1/10. "Before anyone computes: roughly how big?" — about 5 × 2 = 10. |
| Developing | 22 | Estimate by rounding each factor to the nearest whole, then compute exactly and compare. Four items. Then the error hunt: six worked solutions on the board, three of them wrong — one that multiplied the whole parts, one that cancelled top with top, one that forgot to simplify. Pairs find them and say which error each is. |
| Generalising | 8 | The estimate cannot tell you the answer, but it reliably tells you when the answer is impossible. 2½ × 1⅓ = 2⅙ fails the estimate — 2½ × 1⅓ must exceed 2½, and 2⅙ does not. Day 1's misconception is detectable by Day 4's habit. |
| Evaluating | 5 | Exit ticket: estimate, then compute 3¼ × 2⅖. |
Estimates and exact values used (for the teacher):
| Problem | Estimate | Exact | Simplest form |
|---|---|---|---|
| 4⅞ × 2 1/10 | 5 × 2 = 10 | 39/8 × 21/10 = 819/80 | 10 19/80 |
| 3¼ × 2⅖ | 3 × 2 = 6 | 13/4 × 12/5 = 156/20 | 7 4/5 |
| 1⅞ × 4 | 2 × 4 = 8 | 15/8 × 4 = 60/8 | 7½ |
| 2⅓ × 3⅗ | 2 × 4 = 8 | 7/3 × 18/5 = 126/15 | 8 2/5 |
Estimating by rounding both factors down understates, both up overstates. 3¼ × 2⅖ rounds to 6 but is 7⅘ — a 30% gap. Say so out loud: the estimate is a sanity check, not an approximation. Learners who expect it to be close will stop trusting it.
Day 5 · Choosing the method, and the weekly check
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | The class sentence, then two products. |
| Purpose | 4 | Board: "A tricycle uses 2½ litres of fuel per trip. It makes 3¾ trips' worth of driving in a morning. How much fuel?" |
| Developing | 16 | Four word problems in pairs. The taught skill is deciding what to multiply, then estimating, then computing. Learners must write the estimate before the working, in a separate box, so it cannot be back-filled. |
| Weekly check | 15 | Ten items — assessment.md §6. Written Works. |
| Closing | 5 | Day 1 exit tickets returned. Learners write one line: "On Monday I thought ______. Now I know ______." |
Word problems used (answers for the teacher):
| Problem | Working | Answer |
|---|---|---|
| 2½ L per trip, 3¾ trips | 5/2 × 15/4 = 75/8 | 9⅜ L |
| A lot is 2¼ hectares; ⅔ is planted | 9/4 × 2/3 = 18/12 | 1½ hectares |
| Cloth costs ₱120 per metre; 3⅖ metres bought | 120 × 17/5 = 2040/5 | ₱408 |
| A recipe serving 8 is made 1½ times; it used ⅔ kg rice | 3/2 × 2/3 = 1 | 1 kg |
A — ASSESSMENT
A. Formative — not graded, used to steer
| Day | Evidence gathered | What it tells you |
|---|---|---|
| 1 | How many produced 2⅙, counted before the rectangle | How widespread the part-by-part error is in this class |
| 1 | Exit ticket — 1½ × 2¼ with a size judgement | Whether the rectangle changed the method or only this answer |
| 2 | Exit ticket — 3⅓ × 1½ | Whether conversion is reliable under a whole-number answer |
| 3 | Exit ticket — 3⅗ × 1⅔ simplifying first | Whether cancelling is understood or copied |
| 4 | The error hunt — which error was named, not just that one was found | Whether learners can diagnose, which is what marking their own work needs |
| 5 | The estimate box, written before the working | Whether estimating has become a habit or a hoop |
The single most useful check all week is Day 4's error hunt. A learner who can find a wrong answer but cannot name the error will not catch it in their own work, where there is no red pen pointing at it.
Also available all week: the Teacher Panel in game.html reports per-round
accuracy per learner in under a minute, without marking a single paper.
B. Summative — graded, per DO No. 015, s. 2026
Mathematics is a Key Stage 2 core learning area: Written Works 20% · Performance Tasks 50% · Examinations 30%.
| Instrument | Component | Where |
|---|---|---|
| Worksheet §A–C, and the Day 5 weekly check | Written Works | worksheet.html · assessment.md §6 |
| Summative Test 2 — end of Week 10, 20 items | Examinations (30% of the component) | assessment.md §4 |
| Term 1 Examination — end-of-term block, 40 items | Examinations (40% of the component) | assessment.md §5 |
| Group Activity 1 and 2 | Performance Tasks | rubrics in assessment.md §7 |
| The Tile Budget (term task) | Performance Tasks | rubric in assessment.md §7 |
This week's content is examined in Summative Test 2, which covers Weeks 6–10; Summative Test 1 has already been sat at the end of Week 5.
Recording and transmutation: class-record.html, which carries the
SY 2026–2027 adjusted table and the SY 2027–2028 zero-based rule as a switch.
C. Success criteria for the week
The week has succeeded if a learner can:
- Multiply any combination — fraction, whole number, mixed number — and give the simplest form
- Convert fluently in both directions between mixed and improper
- Estimate first, and notice when the exact answer contradicts the estimate
- Say why multiplying the whole parts and the fraction parts separately does not work
Criterion 4 is the one that predicts next week and Grade 7. A learner who has 1–3 by procedure will meet division of mixed numbers in Week 9 and try the same part-by-part shortcut, where the estimate will not save them.
W — WAYS FORWARD
A. Remediation — for learners still producing part-by-part answers after Day 2
Do not re-teach the rule. Re-teach the rectangle, concretely:
- Squared paper, one problem: 1½ × 2½. Count the squares and the part-squares. The answer (3¾) is reachable by counting alone, with no multiplication at all.
- Conversion drilled on its own, away from any product: mixed → improper, twenty items, halves and quarters only.
- Ten minutes during Day 3 and Day 4 independent work, small group, while the rest work on.
B. Enrichment — for learners secure by Day 2
- "Find two mixed numbers whose product is exactly 6. Now find a different pair."
- "2½ × 1⅗ = 4. Explain, without computing, why the answer had to be a whole number." (5/2 × 8/5 — the 5s cancel.)
- The four-piece rectangle written as (2 + ½)(1 + ⅓). This is the distributive law, and it is exactly the Grade 8 expansion of (a + b)(c + d). Learners who see it here meet binomial multiplication as an old friend.
- Game Round 3 from Day 2 rather than Day 4.
C. Differentiation held all week
| Group | Adjustment | Same competency? |
|---|---|---|
| Below level | Halves and quarters only; conversion table on the desk; squared paper for every product | Yes — magnitudes reduced, reasoning identical |
| On level | As written | Yes |
| Above level | Whole-number-answer hunts, the (a + b)(c + d) link, Round 3 from Day 2 | Yes — extended by depth |
| Language support | Improper is explained before it is used; a learner may reason aloud in the mother tongue before writing in English | Yes |
| Additional needs | Enlarged squared paper; verbal exit ticket; peer scribe; a printed mixed-to-improper conversion strip | Yes |
D. Teacher's reflection
To be completed after Day 5.
| Learners meeting the week's intentions | ______ of ______ |
| How many produced 2⅙ on Day 1? | ______ of ______ |
| Named for remediation | |
| Did the four-piece rectangle land, or was it watched rather than understood? | |
| Which day ran over, and what was cut | |
| Did anyone reach the (a + b)(c + d) connection unprompted? | Names. That is Grade 8 arriving early and it is worth feeding |
| Did the estimate box get filled in honestly, or after the fact? | If after, make it a different colour of pen next cycle |
E. Next week
Week 8 pairs competencies 10 and 12 — problems involving division of decimals, and multi-step problems with mixed combinations. Week 9 then takes 13 and 14, division of combinations, which is this week's method plus one inversion. If §C criterion 4 is not met for most of the class, spend Day 1 of Week 8 on this week's content instead; Week 8 is a merged week already, but Week 33 is the one carrying three competencies and is where slack should be taken from if Term 3 allows.
Part of the E-turo MATATAG artifact set. Companion files:
lesson-plan.md (Day 1, Lesson Exemplar format) ·
syllabus.md · assessment.md ·
worksheet.html · slides.html ·
game.html · offline-activities.md ·
class-record.html